Heat half of the oil in a large skillet over medium heat. Once oil is shimmering, add the garlic, red pepper flakes, and Brussels sprouts to the pan and season with salt and pepper. Cook for 5-7 minutes, tossing frequently. Cover with a lid and add vegetable broth if the sprouts start to stick to the bottom of the pan.
Meanwhile, whisk together the vegetable broth and maple syrup in a small bowl and set aside.
Once Brussels sprouts are more fork tender and lightly browned, add the ham and drizzle with the maple syrup broth. Toss to combine thoroughly and cook for 3 minutes or until the broth reduces and thickens. Pour the mixture into a large mixing bowl and add the apple noodles and toss OR if serving as a meal, divide brussels sprouts and ham mixture into bowls and top with apple noodles. Serve.